Interval Estimation for Robust Versions of Lorenz Curve IntegratingEmpirical Likelihood Framework With Influence Functions. - De Mel, Withanage Ajith Raveendra; Sathsarani, T. L. S. M (Computational Engineering and Technology Innovations, 2025)
Real-world data often pose significant challenges for statistical inference due to issues like outliers,violation of classical assumptions, and inherent heterogeneity. Traditional parametric methods,heavily reliant on assumptions such as normality and homoscedasticity, frequently yield unreliableresults when applied to skewed distributions, exemplified by income data with extremely high earners.Empirical likelihood methods have gained prominence to overcome these limitations as they reducedependence on strict distributional assumptions. Further robustness is achieved by incorporatinginfluence functions into empirical likelihood frameworks, explicitly quantifying estimator sensitivityto data contamination, and improving inference reliability. The Lorenz curve is a crucial economicmeasure of income and wealth disparity, but is sensitive to skewness and outliers. This study introducesrobust quantile-based estimators for the Lorenz curve by integrating empirical likelihood and influencefunction methodologies. Confidence intervals are constructed through empirical likelihood optimizationusing a Lagrange multiplier framework and are evaluated against three bootstrap methods. Extensivesimulations reflecting realistic income distributions demonstrate that the influence function-basedempirical likelihood method significantly outperforms traditional empirical likelihood and otherstatistical approaches. Its superior robustness arises primarily from effectively mitigating the distortiveeffects of extreme observations. Consequently, this approach ensures reliable inference even underchallenging real-world conditions characterized by data abnormalities. Nevertheless, the proposedmethods present limitations, notably computational complexity and sensitivity to the assumptionsunderlying influence functions. Future research should expand its application across socioeconomiccontexts, improve computational efficiency, and deepen theoretical and empirical exploration. Thisframework equips researchers and policymakers with precise tools to measure and analyze income inequality.